Accessing plane track using Python API
Works for me in 2.69:

&gt;&gt;&gt; bpy.data.movieclips[0].tracking.plane_tracks.active.markers[0].corners[0][:]
#(0.12633077800273895, 0.4383348524570465)


plane_tracks.active gives me the correct name, even if I rename it in the right sidebar of the movieclip editor. You could try plane_tracks["Plane Track"] or plane_tracks[0] instead.

Do should deselect all in the movieclip editor and re-select the tracking plane and see if plane_track.active changes to the correct name.

clip = bpy.data.movieclips["1100wbdc0000.jpeg"]
print("\nMovie Clip %s" % clip.name)

for i, ob in enumerate(clip.tracking.objects):
    print("\n\tTracking Object %s" % ob.name)

    for j, pt in enumerate(ob.plane_tracks):
        print("\t\tPlane Track %i" % j)

        for k, marker in enumerate(pt.markers):
            print("\t\t\tMarker %i" % k)

            for l, corner in enumerate(marker.corners):
                print("\t\t\t\tCorner %i = %f / %f" % (l, corner[0], corner[1]))